but we have told trainer that we are looking and asked for her input but she doesn't seem interested in helping.
This is kind of a red flag for me. Any idea why she's not interested in helping? Is her business geared just to lessons on school horses? Has she helped other students transition to horse ownership? Is she reluctant because she doesn't think you're ready, or because she doesn't think it's realistic to find something that suits both of you? Or is she just too busy to committ the time? (Yes, it's a major time committent.)
In order increase the odds of this being a successful venture, you need to have a professional both helping you look and helping you with the transition to ownership. If this person your current instructor isn't willing to do that, I'd look for a new barn or new instructor first, and the horse second.
Most horses of the type you'll be looking for and need change hands without every being advertised. They change hands within a barn or are leased to a succession of clients, or are sold by word of mouth through the trainer's/instructor's network. So you need to get plugged into those sources rather than just scanning ads.
I would also strongly recommend you consider leasing before making the jump to ownership. The transition from riding school horses in lessons to riding a your own, fresh horse unsupervised can be a big step; leasing a horse provides an intermediate step.
I'd recommend not going to look at, or ride, advertised horses on your own, and not to put your daughter on anything that hasn't been thoroughly tried out/warmed up first. It's best if you have an instructor, other professional or knowledgable friend with you, and *always* have the seller ride the horse or have it ridden before you do.
To piggyback on what Anabel said above, you want a horse with appropriate experience, and you need to be prepared to pay for that experience. This is not a place to cut corners. As a very general rule of thumb, in my area, a nice, safe horse suitable for a first time owner is $1500 -$2500. If it's decent looking, under 12, sound, and able to do small, local shows, it's $2500 - $5000. Older horses with minor soundess issues may be cheaper, and they may be the perfect compromise for you. However, don't compromise on experience, safety or ground manners.
If you can provide your general location, I can provide some more specific recommendations.